This is Series Resonant Oscillator with Series resonant Xtal with very low Rs. Non-inverting current gain via Q2-E and non-inverting voltage gain Q1-E to Q1-C.
Both Bases are biased around 4V with Q2 saturated until it starts up. Q2-C is inverted outside the loop and is probably pretty ugly looking square wave with lots of droop from 10pF with 240 on the collector and 90 on the emitter.
It would look much better with 1k on Q2-C with a 4.5V square wave with more V gain on Q2 or maybe change Re from 91 to 50 Ohms to get more gain.
These drove the Xtals with pretty high power and would be the huge HC-49 cans with big wafers, so modern microslice xtals might fail in this circuit.